Exercise: 1: Basics of Demand and Supply

1.Given the following demand schedule of a commodity show that by substituting the prices
given in the table into the following demand equation or function, you obtain the corresponding
quantities demanded given in the table:

Price Demand(millions)
(Taka)
6 0
5 10
4 20
3 30
2 40
1 50
0 60

QD = 60 – 10P [ Based on the above schedule]

2. (a) Derive the demand schedule from the following demand function: QD = 80 – 10P. (b)
On the same graph plot the demand schedule of problem 1 and level it D and the demand
curve of part (a) of this problem and label it D1. Does D1 represent an increase in
demand or an increase in the quantity demanded? Why?

Original Demand = 60 -10P ; P = Taka 2 ; Qd = 40

New : QD = 80 – 10P; P = Taka 2 ; Qd = 60
[ shift of the demand curve to the right; change of demand]

3. (a) Derive the supply schedule from the following supply function: Qs = 10P. (b) Derive
the supply schedule from the following supply function: Qs’ = 20+ 10P. On the same
graph plot the supply of part (a) and label is S and the supply curve of part (b) and label it
S1. Does S1 represent an increase in supply or an increase in the quantity supplied? Why?

Qs = 10P

P Q
0 0
1 10
2 20
3 30
 Qs = 10P ; let P = Taka 3; Qs = 30
New Qs = 20+ 10P; P = Taka 3 ; Qs = 20+10*3 = 50 [ shifts (rightward) of the supply
curve]

Qs = 10P

P Qs
0 0
1 10
2 20
3 30
4 40
5 50

Qs’ = 20+ 10P

Qs = 20+ 20*3 = 80

4. Demand, Supply and Elasticity

Price (Taka) Demand(millions) Supply (millions)

60 (Ceiling price 22 14
for gas)
80 20 16
100 18 18
120 [ Floor Price 16 20
for electricity]

a. Calculate the price elasticity of demand when the price is Taka 80 and Taka 100. [
Elasticity in between price Taka 80 and 100; Use Arc elasticity]

b. Calculate the price elasticity of supply when the price is Taka 80 and Taka 100.

c. What are the equilibrium price and quantity? [ d = s]

d. Suppose the government sets a price ceiling (Maximum Price supplier may charge to the
buyers) of Taka 80. Will there be shortage, and if so, how large will it be? Suppose the
government sets a floor price (minimum price supplier should charge to the buyers) of
Taka 120

(a) Calculate the price elasticity of demand when the price is Taka 80 and Taka 100.
 Elasticity of demand = Slope * P/Q = -0.1*80/20 =

Supply Equation = Qs = f(P) = a+ bP = a+ 0.1P;

b = 16-14/80 -60 = 2/20 = 0.1

price = Taka 60, Qs = 14 = a+ 0.1P a+ 0.1*60;

a = 8; Qs = 8 +0.1P

(b) Calculate the price elasticity of supply when the price is Taka 80 and Taka 100.

Supply Equation = 8 +0.1P

Es = Slope * P/Q = 0.1 * 80/16 =

ANS: (c)

Find Demand Equation = 28 - 0.1P [ P1 = 60, Q1 = 22, P2 = 80, Q2 = 20]

Supply Equation = 8 +0.1P [P1 = 60, Q1 = 14, P2 = 80, Q2 = 16]

D=S

28 - 0.1P = 8 +0.1P

P = 100; D = 28 - 0.1P = 28 -0.1*100 = 18 ; S = 8 +0.1P = 8+ 0.1*100 = 18

5. The for mobile homes have been estimated as : Qd  250,000  35P . If this
relationship remains approximately valid in the future:

(i) How many homes would be demanded at a price of $2,000 and $4,000?

(ii) What is the arc elasticity of demand between $2,000 and $4,000? [

Arc elasticity= Slope*Average price/Average Qd

= -35*(2000+4000)/2/(180000+110000)/2 [ If P = $ 2, 000; Qd = 250, 000 – 35 *

2000 = 180, 000; P = $ 4,000; Qd = 250, 000 – 35 * 4000 = 110, 000]

= -35*6000/290000 = - 0.72 [ product is normal; absolute value is less than 1;

Inelastic demand]
(iii) What is the point elasticity of demand at $2,000 and $4,000?

(iv) If 25,000 homes were sold last year, would you expect the average price to have
been? [ Qd = 250, 000 – 35P; 25,000 = 250, 000 – 35P; Solve for P ; 35P = 250,
000 – 25,000 ; 35P = 225,000 ; Find P = ?

6. In the year 2014-15, the demand function for rice in Dhaka is: P = 12.4 - 4Qd and the
supply function is P = -2.6 +2Qs. Work out the equilibrium quantity of Rice sold in
Dhaka in 2014-15.

7. Qd = 10 -4P and Qs = -2+8P. Solve for equilibrium price and quantity demand and
supplied at equilibrium price. Now assume that after imposition of excise tax (collected
from sellers) now supply curve appears as Qs = -8+8P. Find solve for equilibrium price
and quantity demand and supplied at new equilibrium price. [ d =s’ solve, then d = new
supply, solve]
Exercise: 2 [ELASTICITY]

1. Using the following figure calculate the point elasticity at points A and B. What would be
the arc elasticity in this case? Show your computations.

Slope = 11/22 = ½; Take its inverse = 2; Take negative sign [ law of demand; price
and quantity negatively related]; slope = -2

2. Using the following table calculate price point price elasticity of demand (PED), income
elasticity (EM), and cross elasticity (EXY).

PX Py M (= Income) QX
10 9 350 5
9 12 300 6

PED = Slope *P/Q = Change of Qx/Change of Px * Px/Qx = (6-5)/(9 -10) * 10/5 =

EM = Slope *M/Q= Change of Qx/Change of M* M/Qx = (6-5)/(300- 350) * 350/5
EXY = Slope *Py/Q= (6-5)/(12-9) *9/5 = Change of Qx/Change of Py * Py/Qx

For arc elasticity:

PED ( ARC) = (6-5)/(9 -10) * (10+ 9)2 / ( 6+5)/2 =

3. The R.J. Smith Corporation is a publisher of romance novels-nothing exotic or erotic –

just stories of common people falling in and out of fascination. The corporation hires you
as an economist to determine the demand of its product. After months of hard work and
submission of an exorbitant bill,, you suggest the company that the demand for the firm’s
novels (Qx) is given by the following equation:
𝑄𝑥 = 12,000 − 5,000𝑃𝑥 + 5𝑀 + 500𝑃𝑌 [Estimated equation]

Assume that the initial values of Px, M, and Py are Taka 5, Taka 10,000 and Taka 1
respectively. Determine the effect of a price increase would have on total revenue (TR).
 Qx = 12000 – 5000*5+ 5*10,000+ 500*1 = 37, 500 [ Forecasted demand]

Ed = Elasticity of demand = Slope *P/Q = -5000*5/37500 = - 0.67 [ Ed<1, if we

increase price revenue should go up]

Exy = Cross elasticity = Slope * Py/Qx = 500*1/37,500 = + 0.013 [ substitute product]

EI = EM = Income elasticity = Slope * M/Q = 5*10,00/37,500 = 1.33 [ + and greater
than 1, luxury product]

4. The following log-linear demand curve for a price-setting firm is estimated using the ordinary least-squares method:

Q  aP b M c PRd [ Non- Linear Equation ]

lnQ = lna + blnP + cLnM + dlnPr [ Make it linear and both sides make in % form]

[Ed = % Change in Q/% Change in P

Following are the results of this estimation:

DEPENDENT R-SQAURE F-RATIO P-VALUE ON F

VARIABLE: LNQ
OBSERVATIONS 25 0.8587 89.165 0.0001
PARAMETER STANDARD T-RATIO P-VALUE
ESTIMATE ERROR
INTERCEPT 6.77 4.01 1.69 0.0984
LNP -1.68 (b) 0.7 -2.40 0.0207
LNM -0.82 (c) 0.22 -3.73 0.0005
LNPR 1.35 (d) 0.75 1.80 0.0787

The estimated demand equation can be expressed in natural logarithms

lnQ = lna + blnP + cLnM + dlnPr

LnQ = 6.77 -1.68lnP - 0.82LnM +1.35LnPR

Does the parameter estimate for b have the expected sign? Explain. Given these parameter
estimates, is the good normal or inferior good? Explain.
Which of the parameter estimates are statistically significant at 5 percent level of significance?

A 20 percent decrease in household income, holding all other things constant, will cause quantity
demand to change by what percentage and in which direction?

All else constant, a 10 percent increase in price causes quantity demanded to change by what
percentage and in what direction?
The price Elasticity of demand [ -1.67] The cross-price elasticity of demand [1.35 ]The income
elasticity of demand [ -0.82].

A 10 percent decrease in household income, holding all other factors constant, will cause
quantity demand to-----------(increase, decrease ) by-------------percent. A 5 percent decrease
in the price of related good, R, household income, holding all other factors constant, will cause
quantity demand to-----------(increase, decrease ) by-------------percent.

M = -20%; If income decreases by 20%, what will happen to demand?

EM = -0.82 = % Change in QD/ % Change in M

% Change in QD = Given percentage change * Given elasticity = -20%* - 0.82 = + 16.4%

………………………………………………………………………………………………

A 5 percent decrease in the price of related good, R,

% Change in QD = (-5%)* (-1.68) =

CH:9

CS; PS

Ceiling price and floor

Tax vs subsidy

Price support vs Supply restriction

Tariff vs Import quota

———— 11/8/2020 6:38:57 PM ————————————————————

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Regression Analysis: LNQX versus LNPX, LNM, LNPR

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value

Regression 3 0.614417 0.204806 64.05 0.000
LNPX 1 0.007830 0.007830 2.45 0.156
LNM 1 0.001109 0.001109 0.35 0.572
LNPR 1 0.052218 0.052218 16.33 0.004
Error 8 0.025582 0.003198
Total 11 0.639999

Model Summary

S R-sq R-sq(adj) R-sq(pred)

0.0565486 96.00% 94.50% 90.21%

Coefficients

Term Coef SE Coef T-Value P-Value VIF

Constant 7.07 2.63 2.69 0.028
LNPX -0.326 0.208 -1.56 0.156 1.47
LNM -0.513 0.871 -0.59 0.572 16.41
LNPR -2.958 0.732 -4.04 0.004 15.06

Regression Equation

LNQX = 7.07 - 0.326 LNPX - 0.513 LNM - 2.958 LNPR

………………………………………

Following are the results of this estimation:

DEPENDENT R-SQAURE F-RATIO P-VALUE ON F

VARIABLE: LNQ
OBSERVATIONS 25 0.8587 89.165 0.0001
PARAMETER STANDARD T-RATIO P-VALUE
ESTIMATE ERROR
INTERCEPT 6.77 4.01 1.69 0.0984
LNP -1.68 (b) 0.7 -2.40 0.0207
LNM -0.82 (c) 0.22 -3.73 0.0005
LNPR 1.35 (d) 0.75 1.80 0.0787

Take decision based on P-value:

P-Value: It means probability value and it shows the exact risk level with which we can reject
the null hypothesis.

H0: Price has no impact on Qd

Ha: Price has AN impact on Qd

Decision making rule: If P-value is less than 5%, reject the null hypothesis and accept the
alternative hypothesis. In this case P value = 0.02, so we reject the null hypothesis and claim that
Price has a significant impact on Qd.